Answer

$(3m-2)^{2}$

Work Step by Step

You might recognize this a perfect square $(A-B)=A^{2}-2AB+B^{2}$
$ A^{2}=9m^{2}=(3m)^{2}\Rightarrow A=3m$
$B^{2}=4=2^{2}\Rightarrow B=2$
$-2AB=-2(3m)(2)=-12m$
$9m^{2}-12m+4=(3m-2)^{2}$
If you don't recognize the perfect square, factor the trinomial as we have done so up to now:
When factoring $ax^{2}+bx+c$, we search for factors of $ac$ whose sum is $b,$
and, if we find them, we rewrite $bx$ and proceed to factor in groups.
Here, factors of $(9)\times(4)=36$ that add to $-12$ are ....$-6$ and $-6 .$
$9m^{2}-12m+4=9m^{2}-6m-6m+4$
$=3m(3m-2)-2(3m-2)$
$=(3m-2)(3m-2)$
$=(3m-2)^{2}$